Signals & Systems PDF

Module 1 Chapter 1: Signals & Systems Fundamentals of Telecommunication Systems Signal Signal: A signal is a source of information about some physical phenomenon, which varies with respect to time, space or any independent variable​. Hence, a signal is a function of...

Module 1 Chapter 1: Signals & Systems Fundamentals of Telecommunication Systems Signal Signal: A signal is a source of information about some physical phenomenon, which varies with respect to time, space or any independent variable​. Hence, a signal is a function of one or more independent variables. Breaking Down the Definition: Information Physical Phenomenon Varies over Time, Space, Function or Other Dimensions  Measurable aspect of the physical world that can be Physical represented by a numerical value and a unit. Phenomenon: Examples- Temperature, Pressure, Sound, Light, voltage, current, force, velocity, power, density, etc.  Varies Over Time, Space, or Other Dimensions (Function) Function: A relationship that assigns each input to a specific output. Signal is a Function of Time- how a quantity varies over time. Audio signal, Heart rate Signal is a Function of Space- varies across different spatial locations (x, y, z). Image signal, temperature distribution in room Other dimensions- frequency, wavelength, phase, etc Classification of Signals Signals One-dimensional Continuous Time Continuous Valued vs vs vs Multi-dimensional​ Discrete Time ​ Discrete Valued ​ One-dimensional vs Multi-dimensional​ One-dimensional- A signal with one independent variable is called one-dimensional signal. Example: Audio Signal Independent Variable: Time (𝑡) → Function: 𝑓(𝑡) Description: An audio signal represents sound, where the signal's amplitude varies over time. f(t)  One-dimensional vs Multi-dimensional​ Multi-dimensional​ - A signal with more than one independent variable is called multi-dimensional signal. Example: Image, Video​ Image: Independent Variables: Spatial coordinates (x, y) Description: An image is a two-dimensional signal where the pixel intensity varies across the horizontal (x) and vertical (y) dimensions. Function: I(x, y) Video: Independent Variables: Spatial coordinates (x, y), and time (t) Description: A video is a sequence of images (frames) where the pixel intensity varies across both spatial coordinates (x, y) and over time (t). Function: V(x, y, t) Continuous Time vs Discrete Time ​ Continuous Time – A signal with continuous independent variables is said to be continuous time (CT). This means the signal is defined for every value of the independent variable within a given range. Example: Voltage waveform.​ Discrete Time- A signal with discrete independent variables is said to be discrete time (DT). This means the signal is only defined at specific, distinct values of the independent variable. Example: Stock market index​ Continuous Valued vs Discrete Valued ​ Continuous Valued A signal with continuous dependent variable is said to be continuous valued. Example: Voltage waveform.​ Discrete Valued A signal with discrete dependent variable is said to be discrete valued. Example: digital image​ Probable Questions What is a signal? Explain in detail with examples. Give classification of signals based on dimensionality. Explain the classification between continuous and discrete signal with suitable diagrams. Recap Signal: A signal is a source of information about some physical phenomenon, which varies with respect to time, space or any independent variable. Signals One-dimensional Continuous Time Continuous Valued vs vs vs Multi-dimensional​ Discrete Time ​ Discrete Valued ​ Signal Classification Signal Type Time Value Example Continuous Time Continuous Voltage waveform in an electrical circuit Continuous Continuous (any real number- At any moment, the voltage can be any (all moments) Valued (CTCV) infinite values) value along a smooth curve. Clock that chimes every hour, traffic signal, digital clock Continuous Time Discrete Continuous It's continuous in time (it marks every Discrete Valued (specific finite (all moments) hour), but the sound it makes (like a chime) (CTDV) values) is discrete—it's always the same sound each hour. Temperature measurements every hour Discrete Time Continuous Discrete (specific discrete points in time (every hour), but the Continuous Valued (any real number- times) temperature value at each hour can be any (DTCV) infinite values) real number. Counting cars passing a point every minute, Number of Emails Received per Hour, Discrete Time Discrete Discrete Discrete (specific attendance Valued (specific finite times) Times are specific (discrete), and the (DTDV) values) number of cars each minute is a specific number (also discrete). Signal Classification CTCV – Analog Signal DTDV- Digital Systems A system is an entity that processes one or more input signals to produce one or more output signals. ​ Key Characteristics: Input Signal: The signal fed into the system for processing. Output Signal: The signal produced by the system in response to the input. Operation: Systems can modify, filter, enhance, or analyze signals depending on their design and purpose. Classification of Systems Based on Number of inputs and outputs Based on types of signals processed Classification of Systems Based on Number of inputs and outputs Single-Input, Single-Output (SISO) Systems: Process one input signal to produce one output signal. Example: A simple fan speed regulator which controls speed of single fan. Single-Input, Multiple-Output (SIMO) Systems: Process one input signal to produce multiple output signals. Example: A radio broadcasting system where a single audio signal (input) is transmitted simultaneously through multiple antennas (outputs). Multiple-Input, Single-Output (MISO) Systems: Process multiple input signals to produce one output signal. Example: An audio mixing console where several audio sources (inputs) are mixed to produce a single audio output. Multiple-Input, Multiple-Output (MIMO) Systems: Process multiple input signals to produce multiple output signals. Example: cellular base stations (BS) equipped with a very large number of antennas to simultaneously serve many single-antenna users. Classification of Systems Based on types of signals processed One-dimensional or multidimensional One-dimensional system processes signals that vary along a single independent variable. Example- Audio signal processing systems, heart rate monitor Multidimensional system processes signals that vary along multiple independent variables Example- Digital Image, MRI scan, video Analog or Digital Analog system Processes continuous-time-continuous-valued signals Example: Analog audio amplifiers. Digital System Processes discrete-time-discrete-valued signals Example: Digital signal processors (DSPs) used in telecommunications, digital computers  SISO Audio Equalizer SIMO Radio Broadcasting Based on Number of inputs and outputs Environmental MISO Monitoring System Control System for MIMO Autonomous Vehicles Classification of Systems Audio Processing One-dimensional or multidimensional. Image Processing Based on types of signals processed Analog Voltmeter (CT) Analog Telephone Analog or Digital Digital Camera (DT) Digital watch Communication System Signal Processing Systems Signal Processing Systems  Significance of Systems in engineering Engineers build systems that process/manipulate signals. We need a formal mathematical framework for the study of such systems. Such a framework ensures that a system will meet the required specifications (e.g., performance and safety). If a system fails to meet the required specifications or fails to work altogether, negative consequences usually ensue. When a system fails to operate as expected, the consequences can sometimes be catastrophic.  Probable Questions What is a system? Explain the classification of system based on number of inputs and outputs. What is a system? Explain the classification of system based on types of signals processed. Draw neat labelled diagram for different types of systems and explain the significance of systems in engineering.